I have just started. As I went through the vocal warmup in Camille's beginner course my whole body started to tingle. By the end of each warmup run through the tingling was very intense. After a little time of not doing the warm up, body sensations returned to normal.

Is this related to incorrect breathing on my part? Or will this go away with time and practice?

This might be an issue with your breath control or not stretching out your body.

If it's related to breathing, please make sure your breathing is low and relaxed, but not a super big breath to where you are over-breathing. Taking huge breaths or holding your breath could make you light-headed.

Another thing that might be causing the tingling is due to stretching. It could be your body is not accustomed to this yet.

Try breath control first and see if that alleviates the tingling sensations.